I will talk mainly about the first arc, Espoir ship, and a slight spoiler for the second arc in the last paragraph, though only slight.
The anime is about gambling. Kaiji was the guarantor of his friend who disappeared, and now has the debt his friend had. As a jobless man, he has no way to clear this debt in anyway possible. Except if he agrees to what Endou offers, a cruise ship in which he gambles and clears his debt.
From the first 15 minutes of the first episode, we were shown how pathetic Kaiji is, how the lone sharks persuade people into joining their games, and how the world is a wolf in sheep's clothing. No one sides with him, yet Kaiji refuses to believe that.
Then we proceed to the ship, and this is the best part in which I complement in the opening arc. What is the gamble about? restricted Rock-paper-scissors [abbreviated as RPS]. We all know and have played RPS before, while the restricted version is less common but is acceptable and easy to understand since we know everything about the normal RPS.
When they tell Kaiji the rules of gambling, if you were an engaging watcher, then you would have thought of some strategies, especially the 'waste your cards and don't be greedy' strategy. When Funai comes and complements Kaiji for his courage and intelligence, and ridicule the others, he sets up the mood, similar to what Endou did but a different approach, a more passive one. He proposed the strategy mentioned above, and at first it is a great one. But here comes the first mistake, and if you noticed it then well done. Funai proposed a rock>scissors>paper pattern. What is wrong with it? It increases the chances of betrayal, just like what happened. If Kaiji thought for just some little time "to make sure", then he might have refused or changed the pattern to like 4 rocks>4 scissors> 4 papers.
Next, Kaiji teams with his friend and a third person. The third person took a card from them and went to gamble, and lost both the card and the star. Kaiji should have seen the red flag, but ignored it because of the kindness of his heart. Then Kaiji tells them to go and find someone with 9 cards and the last 2 used cards were a rock and a scissor. It is a strange strategy, since it depends on the psyche of the opponent, if he sees through Kaiji's bluff or not. Fortunately, he succeeded and won 2 stars, in which he gave them to his companions (too kind). This strategy high risk/high value, which enforces the thought of gambling in Kaiji.
The next strategy is hoarding rock cards. At first, it is a great strategy, since everyone has to play or else. But now there is another group who discovered this strategy and countered it by hoarding papers. We now see that every strategy we think of, there is a counter to it, and yet sometimes we fail to see it. Kaiji won through intuitive, logic and luck.
After that he hoarded the paper too, so what could be the counter to it? Shuffling! he was forced to shuffle with the others, or he would be deserted and would find no opponents. And who proposed it? Funai! Here we see the first growth Kaiji undergoes, trying to figure what went wrong and how to make use of it. Why did he underwent it, because of a tongue-slip from Funai. He then proceeded to show how he rigged the shuffle to make sure that he will have the upper hand in any opponent aside from Kaiji.
We now see how much depth a simple restricted RPS could be. I could have said a simple game with extreme depth, but I had to showcase the strategies and how much thinking went into it. This is an extraordinary opening arc, in which you will be overconfident at first "it's a RPS game, it's all about luck and some logic since it is restricted". But then we see hoarding, card switching, neutral strategy, guessing the extra card, balanced vs unbalanced decks and predicting or playing around the balanced line of thinking, all of this is showcased in mere 7-9 episodes, in which we don't feel overwhelmed nor bored.
The strategies are not the only good thing about the arc. I did say "to the world", and it is not only about gambling. We see Kaiji's naivety and kindness destroys him many times, and he barely survives. Then we are questioned (not directly, but subtly) should we abandon our morals for the sake of money? If killing someone could get us 20 millions, will we kill him? If everyone does it, is it still okay? Is it okay to trust people? How can Kaiji trusts people after everything he went through? This is the brilliance of the Espoir arc, and the author's greatness at writing characters. Even if some of them were tropes, they were tropes done right.
